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Thanks. I was thinking of using angles, but I'll rethink that. I found another site that had many formulas that were over my head. I think I used the yahoo search engine, advanced search for all the words: vortex shedding sphere force. I'll see if I can find it again.

Originally posted by ben_JD i.e. do vortices shed by prior paintballs further disrupt subsequent paintballs in a long string of shots (indepedent of the subsequent paintball's own vortex shedding issues)?

This is an exaggerated model, due to the objects only being 7 diameters apart, but it is a reference point.

Okay, it appears that a sphere does NOT perform like a cylinder. We have been basing out arguments on cylinder experimentation, which is inaccurate. The problem is that good experimental data for sphere does not appear to exist. Here is what I found:

Based on these studies it is known that vortex shedding in the sphere wake occurs for Reynolds numbers greater than about300. As the Reynolds number is increased beyond this value the vortex shedding process goes through a series of bifurcations which successively increase its complexity.

One characteristic feature of vortex shedding from cylinders is that every shedding cycle involves the formation of two counter-rotating vortices. As a result of this, the lift oscillates at the shedding frequency whereas the drag oscillates at twice the shedding frequency. Thus the cylinder wake exhibits a strong superharmonic component. In contrast vortex shedding from a sphere at low Reynolds numbers involves the formation of one vortex loop per shedding cycle and thus a significant superharmonic component does not exist. This difference between the two wakes is expected to result in a markedly different response to flow perturbations.

All of this was taken from the following link. BJJB, you might want to check out that link, there is much more there including some formulas.

Check my work, please...but it looks like a paintball (.69 inches in diameter) traveling through air at sea level at 300fps will have a Reynolds number of 92,634? Seems high to me, but I am not sure. Most of the articles and theses have been focused on <800 Re.

Also, there are 3.28084 feet in every meter for those of you who (like me) often forget to convert to metric before calculating.

There is some historical, anecdotal evidence for fast firing rates to produce tighter groups. In the early 90's Paintball Consumer Reports International clamped a minimag in a vise with an auto response trigger and fired full speed at a target.

The results stated that the configuration was the most accurate they had ever tested. This is just a commentary without any verification but I thought it was interesting.

I personally think there might be a chance that a drafting paintball might stay in line better. (thats why I always shoot fast )

Originally posted by ben_JD
Check my work, please...but it looks like a paintball (.69 inches in diameter) traveling through air at sea level at 300fps will have a Reynolds number of 92,634? Seems high to me, but I am not sure. Most of the articles and theses have been focused on <800 Re.

Yep, that's a reasonable value. The formula I used includes fluid density in the numerator (air is around 1.23 kg/m^3), so my numbers will be a bit higher than yours.

A lot of the articles deal with slow moving objects (and thus low Re values) because they are much, much eaiser to collect data from.

For those following the entire thread, I did finally conclude that the variable corresponding to the paintball's dimensions was supposed to be its diameter, not its radius. Thus my 50,000 or therabouts Reynolds number value should actually be 100,000 or therabouts.

Originally posted by hitech Okay, it appears that a sphere does NOT perform like a cylinder. We have been basing out arguments on cylinder experimentation, which is inaccurate. The problem is that good experimental data for sphere does not appear to exist. Here is what I found:

[Snip of quoted material]

All of this was taken from the following link. BJJB, you might want to check out that link, there is much more there including some formulas.

That's some good stuff there, though it is a bit beyond my understanding in places. I never did learn much about fluid dynamics. However, the 3-d plots at the end of the document were worth a zillion words towards convincing me that at high Re values the vortex shedding around a sphere becomes chaotic. It actually makes sense on a less technical level if you think of it in terms of "where on the surface can vortices be shed?"

On a cylindrical surface, you basically have two choices... a vortex can shed from the top or the bottom semicircle. If the first one sheds off the top, then it is likely that the next one will be off the bottom due to the imbalances created in the airflow. Thus, you end up with a periodic top-bottom-top-bottom... behavior. Slight vortex asymmetries along the axis parallel to the cylinder's axis still result in the vortex shedding from the same side of that cylinder. There's no way for chaotic behavior to build up.

With a spherical surface, you have a whole mess of choices as to where the vortex will shed. When one vortex sheds, any asymmetry in the way it comes off the sphere will influence where the next vortex will shed. A slight shift one side and you're no longer symmetric about the axis of flight, and the next vortex will come off at some goofy angle, and so on, leading to increasingly chaotic behavior. I see it as a physical manifestation of the "butterfly wingbeats ultimately causing a hurricane halfway around the world" concept often tossed about in studies of chaos.

I'll buy that the orientations of vortices shed from spheres at high Re values are chaotic in nature.

Now let's find a good reference for the force imparted by one of these vortices. The last one, while interesting, didn't really help me much since I don't know what I need to multiply their lateral force coefficients by to get a usable force (read "something with Newtons as its unit").

If you can't find a good factor to calc the lateral force due to asymetric flow then it might be possible to ball park it. If you take a snap shot of the shedding vortex as it's pealing away you will see that it has somewhat of a wing shape.

There should be laminar flow around the outside of this turbulent area causing the area encompased by the ball and vortex to flow air like a wing. In other words, the air flowing around one side of the ball travels farther than air flowing around the other side. This is how a wing creates lift.

If you can find a wing lift program that we can plug the shape into then it should give us some idea of the lifting force. If you can find a real calculation then forget this.

After my long search...

I'm not sure if this is still relevant but a few pages ago it was asked what the spin imparted on a ball shot from a flatline was. After haggling tippmann tech on the tippmann forums and searching every nook and crannie of the web for this I have found the answer. I belive that the flatline spins balls at around 10,000 rpms.

Originally posted by AGD What are some joys and struggles of your career?
The joys are when you make it work well.
The struggles are when they want it to be a different color

Well if you really want to get rid of the walk you could give it a fin(pic), but it would load very well. You would have to use a clip.

Not very practical either but I haven't said anything in awhile.

Realistically it isn't that hard to fix, you can even do a test. Fill a paintball with a liquid as thin as water and fill another one with power or thick thick paint and you will see the accuracy suffers with the thin one. Whats the name of that one paint that is extremely thick? Isn't it like nelson anarchy?

Newtonian Physics

I have been playing paintball for a few years now, and while I havenít shot every paintball gun out there with every barrel available, I would like to draw some conclusions from my education in physics and mathematics pertaining specifically to Newtonian mechanics. I am not an expert I am just working for my BS right now; however I will state this: isnít a paintball moving 300fps, going to be moving the same 300fps out of an automag, a cocker, an angel, etc? The answer is a quite simple yes it is the same thing. So working off of that as a base lets look at the issue of accuracy, I believe this is a some what overstated area you all have delved into. Yes we want a paintball gun to be accurate, but is a colonial smooth bore musket accurate? Simple answer no, the ball is round hence very poor aerodynamics combined with a vacuum effect sucking on the ďbackĒ of the musket ball. I believe what we need to speak of is squeezing distance out of a paintball. I mean where does Tippman say their flatline barrel is more accurate able to snipe on people? Honestly I have never seen anywhere a statement by Tippman stating such, they do promise adding distance to a paintball by putting induced back spin upon the paintball, which we have pretty much all seen, but in reality what does this mean? Simple you may get 10ft-20ft out of a shot from a tippman flatline depending on the induced back spin, BUT think about this, when were all in High School we all took pens apart and shot them with our thumbs causing a back spin and the pen casing seemingly floated/flew a distance, but it always pitched sharply if the pen was slightly unbalanced or pushed just slightly off center. Meaning with the backspin put on by a flatline, your looking at a paintballs center axis almost always getting thrown off a dead on accurate center trajectory needed for this alleged accuracy, what we all want is range and accuracy. The above was with a solid spherical body, which a paintball is NOT, a paintball is a liquid filled nearly spherical gelatin shelled concoction. The problem is the discrepancies from paintball to paintball whether or not they were completely filled, whether the shell is more rigid than others, and the actual thickness and weight of shells and fills, not to mention size. We could easily go into material tensor dynamics of shells alone, I mean a shell being hard would be better in the fact it wouldnít deform on air impact if it in fact does, plus any problems with being misshapen do to any other problems such as barrel flaws, gun flaws, and pressure differentials.

Alright first liquid dynamics, paint fills vary from very runny to quite viscous (hence thick fills), The more viscous filled paintballs would hold a spin better but would resist having a spin initially put on it, which would mean less spin, but a higher fill momentum, this certainly applies to completely filled paintballs with no air. Air or empty space within the paintball would cause horrendous changes within the paintball, primarily dealing with throwing off the center of gravity of the paintball hence causing them to fly over a very broad pattern. The lighter thinner fills would accept a spin more readily but would slow down rapidly, and again the empty space would cause center of mass problems. One simple solution for range and accuracy would be buy viscous fill paintballs, and weigh paintballs, find the heaviest densest brands, this will certainly help. Simple physics on that one, something with a heavier mass moving at one speed compared to a lighter object moving at an equal speed, the object with heavier mass will go farther, because it has a greater momentum. P=m*v

Gelatin shells, well what are you going to do on that one? Most players want brittle shells, which will pop on anything, the problem is this causes problems with it deforming and frankly not making it out of the barrel, we all know about that. The solution is settle for something in between. While we are on the topic, what is better for a shell? Something like RPS makes with a non sticky shell, or the generic familiar shell with the semi sticky outside? Well for one it would be more efficient to have a low coefficient of friction as far as gas savings, but would it be so significant that it would make one superior to another? Probably not, but hey it couldnít hurt right? Lower coefficient of friction means less rubbing, meaning less chances of breaking a ball, and imparting unwanted spin hence more accuracy and possible range. Also the question of seams and this is just from experience and brands, large seams are not good, however they seem to be necessary (no pun intended) for accuracy and efficiency, they act very similar to grooving of a musket ball just in reverse. I donít believe they cause spin directly, simple friction causes this regardless of seams or not. Truthfully everything I have ever played with has seams, some are just hidden better by another coating of some material, and however it does leave a bulging along the ďequatorĒ, which might as well be a seam. I truthfully donít have any conclusive answers on that one, but I have never seen any difference with the many various brands and grades of paint I have shot, other than big seams in my opinion seem to cause inaccuracy.

Bolt systems, which is superior? Frankly the most simplistic, lightest weight, efficient designed system one can get on their marker. Personally I feel AGD is superior with theirs simply because it allows excellent BPS, accuracy, and efficiency. Does this negate people who own cockers, or have blow backs or the various other styles? Of course not truly what I said before is what goes 300fps out of a cocker, automag, angel, tippman, etc, is still 300FPS bottom line, is the paint and barrel going to make some of the deciding factor on range and accuracy yes, but simply if velocity is held constant and the mass of the paintball is the same then the momentum will be the same so holding the guns at the same angle in a perfectly controlled environment they will go roughly the same distance simple damned physics. Hence I am tired of everyone telling me how damned much range they have on their autococker, try this on: if you played towards the front as opposed to hiding in the back, then possibly out of the 4 hoppers of paint you have been shooting at me, maybe one would break on me for a change eh? (yes slanted personal opinion, but who else is getting tied of it?) I mean going back to momentum, certain paintballs needs more momentum then others to break and by the time your paint has allegedly gone half or all the way down the field the kinetic energy and momentum that were imparted on the ball to begin with have greatly decreased from what they were, simply meaning there is a significant chance the paintball will not break on the desired person not to mention it isnít brute forcing the air out of itís way towards the end of itís trajectory. I mean we have all played on a windy day, itís the 2nd half of the trajectory that gets greatly affected depending on how high the wind is, this is simply because the momentum has greatly decreased than in the beginning of itís flight. This is really Newtonian Mechanics pure and simple, a force or forces is imparted upon the paintball it travels with a decent amount of friction down a tube and exits with various pressure differentials upon it and of course we arenít talking about a rigid body here, but much closer to a semi-rigid object which literally changes with every new paintball in the barrel consistency is something one just canít expect from paintball, just a close median.

I hope the grammar and spelling in this document arenít too bad, I proof read 4 times and used spell checker, but no promises friends.

PS
I am not sure if anyone else has stumbled upon this, but you can make your E-mag almost into an electric RT by setting your hall sensor back as opposed to forward, and then by simply switching to "hybrid mode" you gently depress your trigger and rid the firing stud that manual mode would normally push, but infact it gently taps your finger and gives you an RT electric. Quite alot of fun to play with, very very wicked on the competition and easily maxes out the Emag rate of fire.

It appears that the side drag coefficients for a sphere are only an order smaller magnitude than the "forward" drag coefficient. While I will have to determine what that really means, I believe THAT IS A HUGE FORCE. If that is true it is amazing that a paintball ever hit anywhere near where it is aimed.

Added on edit: If I am reading correctly the side coefficient is 0.1.

Here is what I found:

The force on the sphere is decomposed into three components: the drag force Fd , which acts in the streamwise (x-) direction, and the two components of the side force (Fy and Fz ), which act perpendicular to the drag force. The magnitude of the side force can be computed as Fs?(Fy^2 + Fz^2). Figure 1 shows the variation of the drag Cd and side force Cs coefficients with time. The mean values of the drag coefficient for Re = 500, 650, and 1000 are computed to be 0.56, 0.52, and 0.47, respectively, and these are in very good agreement with experiments. The side-force coefficients show a complex behavior with magnitudes that are roughly an order smaller than those of the drag coefficient.

I hereby nominate Hitech for the "most diligent information gatherer of the year" award. How in the world did you find those two .pdf reports? I gave up a couple of weeks ago after no luck in finding anything concerning lateral forces on spheres. I am impressed!

Originally posted by hitech It appears that the side drag coefficients for a sphere are only an order smaller magnitude than the "forward" drag coefficient. While I will have to determine what that really means, I believe THAT IS A HUGE FORCE. If that is true it is amazing that a paintball ever hit anywhere near where it is aimed.

Added on edit: If I am reading correctly the side coefficient is 0.1.

I would give the coefficient (Cs) an average value of around 0.06, judging from figure 1 in the file AIAA_Apr_2002.pdf.

To determine what this means, you need to plug that coefficient into a drag-like force equation; here ya go:

Fs = 0.5 * rho * V^2 * Cs * A, where

Fs is the side force experienced by the paintball,
rho is the density of the air (around 1.239 kg/m^3),
V is the velocity of the air relative to the paintball (around 85.3 m/s for a 280 fps shot),
Cs is the side force coefficient (around 0.06), and
A is the cross sectional area of the paintball (around 0.000234 m^2).

Plug in the numbers, stir gently, and you get a side force of around 0.063 newtons.

What does this mean? Well, let's see what we get for a lateral acceleration resulting from this side force. F = m * a is all we need. The mass of a paintball is around 0.003 kg.

a = F/m
a = 0.063 / 0.003 = 21.1 m/s^2

21 meters per second squared for a lateral acceleration... that's over 2 g's of sideways acceleration this thing is experiencing, and that's for only one shed vortex. There are a couple/few hundred shed vortices during the flight of a paintball. About the only thing that helps us get some level of accuracy out of a paintball is that those vortices seem to be shed in random orientations.

If I get a chance this weekend, I'll see what I can do about generating a random walk using this type of data. The walk will be a random direction walk using random step sizes. We can then plug the results of that walk into a motion model to see where the paintball should fall. Rinse/repeat several times and you end up with a distribution function describing where a paintball will likely strike relative to its aim point.

It's been so long since the beginning of this thread (and the thread that spawned this one) that I don't remember what my original thoughts re. barrels actually were.

Something popped into my head while writing the above sentence...

We have determined that spin itself does not significantly affect the paintball's trajectory at the spin rates seen coming out of a normal barrel (i.e. not a barrel specifically designed to induce spin). We used something akin to Bernoulli's equations to determine the effects of spin on a paintball's trajectory. The calculated trajectory effects were significantly less than the deviations found in AGD's tests.

So a low spin rate Bernoulli-type differential airflow was not enough to screw up a paintball's flight. However, could that small amount of spin actually induce a preference in the way vortices are shed from the paintball? With no spin, vortex shedding is essentially random in orientation for spheres at these high Reynolds numbers; perhaps spin adds a bit of a bias in the vortex shedding orientation. We see that the vortices result in approximately 2 g's worth of acceleration each time one is shed, so a slight spin-induced preference in vortex orientation may cause a decrease in accuracy as compared to the no spin, pure random walk case.

And here I thought this thread was dead! Hitech, man I have to hand it to you, you truely are the KING of internet searches! You should go out on the net and look for a pot of gold!

Its just incredible that we have some kind of number for the side force on the ball. This thread has gone so much farther than we took the research that I am incredibly impressed. Then again when we did the tests we didn't have the net

So if Bjj can come up with a random walk program we will actually have a mathematical formula that characterizes paintball accuracy! (and it doesn't include a barrel).

I posted this thread up on the main forum in hopes that the general paintball populace would read it. Again if I had any marketing sense I would have known that they really don't care. So it remains to the few to delve into the unknown in search of knowledge.........

Originally posted by luke I don't think that's a fair statement. I think it's more that the technical jargon is TOO far over everyone's head. I am interested in the final answer though.

I think it is quite fair. The only "training" I have is a Junior College Physics class. Otherwise I write computer programs for a living.

In simple terms what makes paintballs so inaccurate is 2Gs worth of laterial (side) force from what is called vortex shedding. There isn't anything a barrel CAN do to affect it. The only difference a barrel can have is more consistant velocity. That makes a small difference. That's it.

When I said "I don't think that's a fair statement" I was referring to Tom's statement "they really don't care." I was implying the debate was over most of our heads, not that we didn't care. In fact, most of us do care in the FINAL ANSWER , we just prefer it in laymen terms.

(look at the hits on the thread, to me that implies people are reading it)

I guess my reasoning for it being a fair statement is that almost every day some asks what barrel is better than another. Read the answers. Everyone thinks that paint to barrel match is king. Why? Does anyone know why? Some believe that it give better velocity consistancy. Anyone ever tested this? My simple observation is that it does NOT. Freaks and other barrel kits are very popular and very expensive. And yet NO ONE knows if they even work. I'll bet they don't make even 0.5% difference. My huge bore stock emag barrel often gives the EXACT same reading over the chrono for two shots. How much more consistant can you get?

BTW, I paid $25 shipped for it. Why, probably because it was ONLY a stock barrel.

I just realized I posted a long discussion that tried to summarize some of the major views on this thread on the wrong forum. My discussion also considered an alternate mechanism for the 114 data.
The discussion is quite long, so I hate to repost it here. Please take a look at the last page of the Paintball Talk forum, Paintball Spin Physics thread. I would certainly like to hear this Group's views.

Oh boy here I go.

Warning:This is not strictly about the title of Spin physics since I think that has been solved,but it does relate to the original question of open and closed bolt and accuracy, and I think it is appropriate to discuss at this point.

Hi All,
I haven't talked about any of this since Deep blue was the fight club,we discussed reynolds factors and turbulence even back then.
I think there is a big part of the equation that is being missed. You have analysed until you are deep blue in the face what happens durring 99.5% of the paintball flight. That once you have a sphere traveling at 280fps, with the current wt of a paintball, you are going to have a certain level of randomness imparted by the turbulence behind the ball. I for one stand up and say bravo. You have explicitly defined something that we cannot change unless we play in a vaccum (deadly), or fundimentally change the paintball (not likely).
You have also effectively eliminated the need for people to worry about spin/rifleing unless the paintball gets heavier, changes shape, or we shoot it a lot faster.

I think Glenn's problem with all of this (not speaking for him of course), and mine, is that we are in an amazing way ignoring that first 12 inches of the balls travel. At this time we are not looking at the simple fluid dynamics of a ball. I am talking about what happens in the marker and in the barrel before it exits and the effect this has on the tragectory of the ball within the barrel and upon its immeadiate exit from the barrel.
This leads us away from much of Tom's data as he used the same gun and barrel for every shot and it was locked in a vise. This means he removed all of the parameters that we can effect and change to improve accuracy. All that was left was the randomness of air currents (Sorry Tom, not meaning to burst this scientific bubble, but I am the Slayer of scared cows, even yours).

So what matters the first 12 inches? Look at what we have.
1. We have a wall of force (air) accelerating the ball into the atmospheric air(no trailing currents there folks) and in some way disipating. Ok, that is why Tom created the Crown point barrel (he must have thought it mattered) and others created the ported barrel. If the barrel is ported and long enough the issues of the initial push may be eliminated (maybe longer barrels are more accurate).
2. We have the barrel. The ball is traveling through the barrel with forces places upon it. One is the force excellerating it, another is the force of the barrel pushing on a larger ball, or the force of the air passing the ball for a smaller ball.
3. We have a moving marker. I know you may think that doesn't matter but we know that a ball can ricochet around in the barrel from Tom's barrel tips and the talc test. The barel might not be perfectly straight or aligned or you may be moving it.
And doing the math:

The diameter of the paintball is 0.68 approx I am not sure of the bore of a 2 step barrel but let us assume 0.7. If the ball is going down the exact center (which I highly doubt considering manufacturing tolerences) that leaves 0.01 inch that the barrel would have to move. The ball is only in the barrel for about 0.006 seconds.
Thats 0.01 inch divided by 0.006 seconds = 1.66 inches per second. All it takes is moving your barrel 0.01 inches at a rate faster than 1.6in/sec. That is while shooting 6 bps of perfect balls out of a perfect barrel to have a hit. I think maybe it hits more than you think.

So what who cares?.... Well you do. These are all elements you can change. They effect what direction the paintball is heading then it leaves the barrel.
So lets say our shot vector is one degree off straight when it leaves the barrel. At 5 feet it is 1 inch off mark, at 50 feet it is 10 inches off mark. Let us say our shot vector is at an angle of 0.5 degrees off center when it exits the barrel. That's 0.5 inch at 5 ft, and 5 inches at 50 ft, and 10 inches off mark at 100ft.

Maybe I am full of it maybe all paintballs leave all barrels and all guns at exactly the same angle. And maybe we always shoot with our gun in exactly the same position, and maybe we never move even 0.01 inch at a rate of 1.6in/sec while taking a shot.

I enjoyed the read on this post it was incredible. Keep up the good work. Now lets look at the other 0.5% of the game and maybe that will make all the difference.
Respectfully,
Your Friend
Hitmanng

Sorry for dropping out, but life an family have taken me out of this for a little bit. I want to drop a VERY quick couple of comments here-

I am completely in awe of the great numbers everybody has come up with, but I did want to reconnect with some thoughts I posted in the beginning.

There is a difference in accuracy, even on bench mounted guns, between different barrels, different markers, and different paint. If we are to acknoweldge the findings from PCRI for accuracy, we need to also acknowledge that all the guns shot different patterns, with some guns being more accurate than others. We have figured out what the ball does after is leaves the barrel, but we are still neglecting that there is something inherent in the action of a specific marker, even bench mounted, that leads to differences in accuracy. Even a clean to dirty barrel will affect the accuracy, and that IS NOT included in any of the numbers brought up yet.

The fore-ball air colume might be a culprit, but also I think we dismissed the balls rotation too quick. If I am allowed to reverse the Tippmann Flatline #'s (if they are correct) here is a quick thought.

10,000 rpm is 166 rotations per second, and at 280 fps, that is 14 ft traveled per second. 168 inches a second. Or about one revolution a inch. How does that affect the air column?

Can anybody figure out the sideload boundy affect knowing the amount the ball is held up and the amount the the ball is rotaing per second? I will clarify after some thought n my own.

Josh

Last edited by pbjosh; 02-24-2003 at 07:04 PM.

"If you build it they will run" - pbjosh
MM006610 bought new in '94. One owner.http://itspaintball.com For Pneu Ideas

Okay. I originally attempted to perform a full-blown simulation incorporating drag force to slow down the paintball, recalculation or the reynolds number at each time step, and a whole mess of other bells-n-whistles. It was a royal pain in the butt trying to keep track of all the variables, and generated results that just didn't make any sense. I had clearly made some errors in my coding somewhere along the way, and I just couldn't seem to track it down.

So, I decided to simplify things... a lot.

The parameters for the simulation are as follows:

1. The ball's axial velocity (U) is a constant 300 fps (91.44 m/s).
2. The Strouhal number (St) used was 0.2.
3. The paintball's diameter was 0.68 inches (0.017272 m).
4. The vortex shedding frequency (St * U / D) was approximately 1000 Hz.
5. The vortex shedding period was approximately 0.001 seconds.
6. The full distance travelled by the ball was 150 feet (45.72 m).
7. The time of flight from barrel exit to target was 0.5 seconds.
8. The number of vortices shed during flight was approximately 500.
9. The air density used was 1.239 kg/m^3.
10. The air viscosity used was 1.73x10^-5.
11. The Reynolds number used was approximately 113000.
12. The dimensionless lateral force coefficient was approximately 0.05.

This gives us a lateral force magnitude of approximately 0.06 Newtons, using the following formula:

13. The paintball's mass was 0.003 kilograms.
14. The lateral acceleration was approximately 20 m/sec^2.

The procedure:
Every time a vortex was shed (every 0.001 seconds according to items 3 and 4 above), a randomly oriented acceleration of 20 m/sec^2 was applied to the paintball. I interpolated between these acceleration "spikes" to generate a random-walk-like pattern.

I converted the acceleration random walk into a velocity walk, and then into a position walk.

I noted the endpoint of this position walk, and then repeated the whole process ten thousand times.

The results:
The following links point to plots of the results...cut-n-paste the URLs if necessary...

From the results of the simulation, I cannot conclude that a series of randomly oriented 2-G "kicks" is sufficient to knock the ball off course to the magnitude seen in AGD's tests. The greatest concentrations of simulated paintball strikes falls around 0.15 millimeters from the aim point... a distance much smaller than that observed in AGD's real data.

I suspect that there is still something else at work here, and I believe that it may lie in the possibility that a slight spin on a paintball would induce a preferential orientation for vortex shedding. This may cause the ball to be repeatedly "kicked" in the same direction and would thus end up with a greater deviation than a purely random "kick" orientation would generate. If the shot-to-shot orientation of slight paintball spin is not constant (and I suspect it's not), this greater deviation would be randomly oriented with respect to the aim point, as opposed to a simple off-center grouping.

It would be interesting to measure the spin orientation for many successive paintball shots to see if the orientation is reasonably constant or reasonably random. Tom, perhaps you could provide a bunch more test photos for measurement?

I originally attempted to perform a full-blown simulation incorporating drag force to slow down the paintball, recalculation or the reynolds number at each time step...

I hadn't thought of that before. However, I don't think you can get meaningful numbers without having the ball slow. Maybe not recalculate at every step, but at least use some predefined changes. Say five or ten different velocities at various points. I don't think we can use a simulation at only 300fps. The paintball has much more momentum at 300fps. Any idea how fast a paintball is traveling after 80 feet?

From the results of the simulation, I cannot conclude that a series of randomly oriented 2-G "kicks" is sufficient to knock the ball off course to the magnitude seen in AGD's tests. The greatest concentrations of simulated paintball strikes falls around 0.15 millimeters from the aim point... a distance much smaller than that observed in AGD's real data.

Am I missing something? As I read your plots and graphs I see more like 2 meters. What am I missing? Also, the problem is quite probably with using the numbers from only 300fps. The real world just isn't neat enough for that.